Question

normal population has a mean of 63 and a standard deviation of 13. You select a random sample of 25. Compute the probability that the sample mean is: (Round your z values to 2 decimal places and final answers to 4 decimal places): Greater than 65.

Answer 1

0.2207

Explanation:

Here, we want to find the probability that the sample mean is greater than 25.

What we use here is the z-scores statistic

Mathematically;

z-score = (x-mean)/SD/√n

From the question;

x = 65, mean = 63, SD = 13 and n = 25

Plugging these values in the z-score equation, we have

Z-score = (65-63)/13/√25 = 2/13/5 = 0.77

So the probability we want to calculate is ;

P(z > 0.77)

This can be obtained from the standard normal distribution table

Thus;

P(z > 0.77) = 0.22065 which is 0.2207 to 4 d.p